Question

$PQRS$ is a cyclic quadrilateral. Find the measure of $\angle P$ and $\angle Q$.

• A. ${135}^{\circ },{60}^{\circ }$
• B. ${60}^{\circ },{120}^{\circ }$
• C. ${60}^{\circ },{90}^{\circ }$
• D. ${100}^{\circ },{120}^{\circ }$

Answer 1

The correct option is A ${135}^{\circ },{60}^{\circ }$

Here, $PQRS$ is a cyclic quadrilateral.

We know, opposite angles of a cyclic quadrailateral are supplementary.
$\therefore 3x+x={180}^{\circ }$ and $2y+y={180}^{\circ }$
$\Rightarrow 4x={180}^{\circ }$ and $3y={180}^{\circ }$
$\Rightarrow x={45}^{\circ }$ and $y={60}^{\circ }$.

$\therefore \angle P=3x=3\times {45}^{\circ }={135}^{\circ }$ and $\angle Q=y={60}^{\circ }$.

Hence, option $A$ is correct.